W-disjoint Orthogonality Research Articles

The effect of source sparsity on independent vector analysis for blind source separation

In this paper, the effect of source sparsity on the performance of the independent vector analysis (IVA) algorithm for blind source separation is investigated. The IVA algorithm was originally developed under the assumption of statistical independence between the sources and has made great advances in recent years. However, its performance under different sparsity conditions is rarely studied. This study begins by mathematically analyzing the performance of IVA in permutation alignment, which is proved to directly correlate with the degree of frame-level W-disjoint orthogonality (F-WDO) of the sources. We further prove that IVA can theoretically achieve the optimal separation in the cases where the sources are F-WDO. Experimental results show a strong positive correlation between a quantitative measure of F-WDO and the IVA algorithm’s performance under various conditions.

Dynamically localizing multiple speakers based on the time-frequency domain

In this study, we present a deep neural network-based online multi-speaker localization algorithm based on a multi-microphone array. Following the W-disjoint orthogonality principle in the spectral domain, time-frequency (TF) bin is dominated by a single speaker and hence by a single direction of arrival (DOA). A fully convolutional network is trained with instantaneous spatial features to estimate the DOA for each TF bin. The high-resolution classification enables the network to accurately and simultaneously localize and track multiple speakers, both static and dynamic. Elaborated experimental study using simulated and real-life recordings in static and dynamic scenarios demonstrates that the proposed algorithm significantly outperforms both classic and recent deep-learning-based algorithms. Finally, as a byproduct, we further show that the proposed method is also capable of separating moving speakers by the application of the obtained TF masks.

Narrowband multi-source direction-of-arrival estimation in the spherical harmonic domain.

A conventional approach to wideband multi-source (MS) direction-of-arrival (DOA) estimation is to perform single source (SS) DOA estimation in time-frequency (TF) bins for which a SS assumption is valid. Such methods use the W-disjoint orthogonality (WDO) assumption due to the speech sparseness. As the number of sources increases, the chance of violating the WDO assumption increases. As shown in the challenging scenarios with multiple simultaneously active sources over a short period of time masking each other, it is possible for a strongly masked source (due to inconsistency of activity or quietness) to be rarely dominant in a TF bin. SS-based DOA estimators fail in the detection or accurate localization of masked sources in such scenarios. Two analytical approaches are proposed for narrowband DOA estimation based on the MS assumption in a bin in the spherical harmonic domain. In the first approach, eigenvalue decomposition is used to decompose a MS scenario into multiple SS scenarios, and a SS-based analytical DOA estimation is performed on each. The second approach analytically estimates two DOAs per bin assuming the presence of two active sources per bin. The evaluation validates the improvement to double accuracy and robustness to sensor noise compared to the baseline methods.

A Source Counting Method Using Acoustic Vector Sensor Based on Sparse Modeling of DOA Histogram

The number of sources present in a mixture is crucial information often assumed to be known or detected by source counting. The existing methods for source counting in underdetermined blind speech separation suffer from the overlapping between sources with low W-disjoint orthogonality. To address this issue, we propose to fit the direction-of-arrival (DOA) histogram with multiple von-Mises density (VM) functions directly and form a sparse recovery problem, where all the source clusters and the sidelobes in the DOA histogram are fitted with VM functions of different spatial parameters. We also developed a formula to perform the source counting taking advantage of the values of the sparse source vector to reduce the influence of sidelobes. Experiments are carried out to evaluate the proposed source counting method, and the results show that the proposed method outperforms two well-known baseline methods.

The Control Packet Collision Avoidance Algorithm for the Underwater Multichannel MAC Protocols via Time-Frequency Masking

Establishing high-speed and reliable underwater acoustic networks among multiunmanned underwater vehicles (UUVs) is basic to realize cooperative and intelligent control among different UUVs. Nevertheless, different from terrestrial network, the propagation speed of the underwater acoustic network is 1500 m/s, which makes the design of the underwater acoustic network MAC protocols a big challenge. In accordance with multichannel MAC protocols, data packets and control packets are transferred through different channels, which lowers the adverse effect of acoustic network and gradually becomes the popular issues of underwater acoustic networks MAC protocol research. In this paper, we proposed a control packet collision avoidance algorithm utilizing time-frequency masking to deal with the control packets collision in the control channel. This algorithm is based on the scarcity of the noncoherent underwater acoustic communication signals, which regards collision avoiding as separation of the mixtures of communication signals from different nodes. We first measure the W-Disjoint Orthogonality of the MFSK signals and the simulation result demonstrates that there exists time-frequency mask which can separate the source signals from the mixture of the communication signals. Then we present a pairwise hydrophones separation system based on deep networks and the location information of the nodes. Consequently, the time-frequency mask can be estimated.

The analysis of the simplification from the ideal ratio to binary mask in signal-to-noise ratio sense

For speech separation systems, the ideal binary mask (IBM) can be viewed as a simplified goal of the ideal ratio mask (IRM) which is derived from Wiener filter. The available research usually verify the rationality of this simplification from the aspect of speech intelligibility. However, the difference between the two masks has not been addressed rigorously in the signal-to-noise ratio (SNR) sense. In this paper, we analytically investigate the difference between the two ideal masks under the assumption of the approximate W-Disjoint Orthogonality (AWDO) which almost holds under many kinds of interference due to the sparse nature of speech. From the analysis, one theoretical upper bound of the difference is obtained under the AWDO assumption. Some other interesting discoveries include a new ratio mask which achieves higher SNR gains than the IRM and the essential relation between the AWDO degree and the SNR gain of the IRM.

The optimal ratio time-frequency mask for speech separation in terms of the signal-to-noise ratio

In this paper, a computational goal for a monaural speech separation system is proposed. Since this goal is derived by maximizing the signal-to-noise ratio (SNR), it is called the optimal ratio mask (ORM). Under the approximate W-Disjoint Orthogonality assumption which almost always holds due to the sparse nature of speech, theoretical analysis shows that the ORM can improve the SNR about 10log(10)2 dB over the ideal ratio mask. With three kinds of real-world interference, the speech separation results of SNR gain and objective quality evaluation demonstrate the correctness of the theoretical analysis, and imply that the ORM achieves a better separation performance.

Time frequency source separation and direction of arrival estimation in a 3D soundscape environment

The DUET (Degenerative Unmixing and Estimation Technique) algorithm has been shown to be an effective method for the separation of multiple sources from a stereo mixture. We present a time–frequency masking technique based on DUET for the blind separation of N sources from a four channel B format audio mixture. This method is applicable where sources that are both radially sparse in three dimensions, and exhibit approximate W-disjoint orthogonality, i.e. where the signals are approximately sparse in the time–frequency domain. Using the B-format mixture, we generate a three dimensional power-weighted geodesic histogram and show the peak locations correspond to the direction of arrival of the sources. These peaks are then used to generate a time–frequency mask to separate the sources from the w-channel of the B-format mixture. Experimental separation results using speech signals are presented.

Harmonic Signals Retrieval Approach Based on Blind Source Separation

A frequently encountered problem in signal processing is harmonic retrieval in additive colored Gaussian or non-Gaussian noise, especially when the frequencies of the harmonic signals are very close in space. The purpose of this paper is to develop an efficient Blind Source Separation (BSS) algorithm from linear mixtures of source signals, which enables to separate harmonic source signals using only one observed channel signal even if the frequencies of the harmonic signals are closely spaced. First, we establish the BSS based harmonic retrieval model in additive noise by using the only one observed channel, and analyze the fundamental principle by utilizing BSS method to retrieve harmonics. Then, we propose a BSS-based approach to the harmonic retrieval by resorting the concept of W-disjoint orthogonality in the over-complete BSS situation, and as a result, we get the separation algorithm using only one channel mixed signals. Simulation results show that the proposed separation algorithm-BSS-HR is able to separate the harmonic source signals.

W-Disjoint Orthogonality Based Residual Acoustic Echo Cancellation for Hands-Free Communication

A simple and novel residual acoustic echo cancellation method that employs binary masking is proposed to enhance the speech quality of hands-free communication in an automobile environment. In general, the W-disjoint orthogonality assumption is used for blind source separation using multi-microphones. However, in this Letter, it is utilized to mask the residual echo component in the time-frequency domain using a single microphone. The experimental results confirm the effectiveness of the proposed method in terms of the echo return loss enhancement and speech enhancement.

Robust Relative Transfer Function Estimation for Dual Microphone-Based Generalized Sidelobe Canceller

In this Letter, a robust system identification method is proposed for the generalized sidelobe canceller using dual microphones. The conventional transfer-function generalized sidelobe canceller employs the non-stationarity characteristics of the speech signal to estimate the relative transfer function and thus is difficult to apply when the noise is also non-stationary. Under the assumption of W-disjoint orthogonality between the speech and the non-stationary noise, the proposed algorithm finds the speech-dominant time-frequency bins of the input signal by inspecting the system output and the inter-microphone time delay. Only these bins are used to estimate the relative transfer function, so reliable estimates can be obtained under non-stationary noise conditions. The experimental results show that the proposed algorithm significantly improves the performance of the transfer-function generalized sidelobe canceller, while only sustaining a modest estimation error in adverse non-stationary noise environments.

Separation of Multiple Speech Signals by usingTriangular Microphone Array

Speech source separation has been an important topic to realize speech-based human-machine interfaces or high quality hand-free communication with machines. For source separation, Independent Component Analysis (ICA) and time-frequency masking are powerful methods as a tool of Blind Source Separation (BSS) of speech mixtures. The latter method is based on the assumption called \W-Disjoint Orthogonality" which implies the cell component sparsity of speech in the time-frequency domain. One of the topics treated in this article is to introduce the time-frequency masking scheme is applied to the equilateral triangular array where the three delay estimates from each microphone pairs are obtained. In addition, it is used to improve histogram-mapping algorithm by integrate and coordinate transformation of three delay estimates. Some experiments in real environment for separating multiple sources are performed to verify the effectiveness.

Blind Separation of Speech Mixtures via Time-Frequency Masking

Binary time-frequency masks are powerful tools for the separation of sources from a single mixture. Perfect demixing via binary time-frequency masks is possible provided the time-frequency representations of the sources do not overlap: a condition we call W-disjoint orthogonality. We introduce here the concept of approximate W-disjoint orthogonality and present experimental results demonstrating the level of approximate W-disjoint orthogonality of speech in mixtures of various orders. The results demonstrate that there exist ideal binary time-frequency masks that can separate several speech signals from one mixture. While determining these masks blindly from just one mixture is an open problem, we show that we can approximate the ideal masks in the case where two anechoic mixtures are provided. Motivated by the maximum likelihood mixing parameter estimators, we define a power weighted two-dimensional (2-D) histogram constructed from the ratio of the time-frequency representations of the mixtures that is shown to have one peak for each source with peak location corresponding to the relative attenuation and delay mixing parameters. The histogram is used to create time-frequency masks that partition one of the mixtures into the original sources. Experimental results on speech mixtures verify the technique. Example demixing results can be found online at http://alum.mit.edu/www/rickard/bss.html.